Global Temperature Increases |
Airport Temperature and Deviation Charts |
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What the Charts DoAirport charts compare temperatures observed in the two weeks prior to July 1, 2013, to normal and extreme temperatures at airports throughout the world. They relate observed temperatures every hour to the normal temperature and the record high and low temperatures approriate for that specific hour. They show the deviations of observed temperatures from the normal daily cycle. Furthermore, they show a two-week average of those deviations to indicate how observed temperatures generally compared to normal in the two weeks prior to July 1, 2013.Temperatures in isolation tell you little. Some reference temperatures are needed to determine if the observed temperature is about normal, much hotter than usual, or colder than average. Being able to make the comparison is complicated by the fact that temperatures vary in a daily cycle because of warming every day by the sun and cooling at night. Weather records will tell you that the high temperature for the day was 86 degrees, the low 45 degrees, and the average 62 degrees, but how does that relate to a temperature of 76 degrees at 11:00 in the morning? Is that hotter or colder than what would be expected at that hour? From only the highest and lowest temperatures for the day, it is very difficult to guess how the temperature at any time of day relates to the historical record. The temperature charts place observed temperatures in the context of the daily cycle so you can tell. They relate what was happening at the time of the temperature observation to the normal, record high, and record low temperatures for that same time. They present the difference between the observed and normal temperatures as a temperature "deviation" showing how many degrees hotter it is than normal -- in red -- or colder than normal -- in blue. Here is an example for Washington, DC. To see more, click |
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The charts allow placing the observed temperature into the proper perspective
for the instant. In addition, for the most recent two weeks, they compare
the pattern of the observed temperatures to the normal temperatures, and to the record
high and low temperatures. If the observed-temperature curve is generally near
the normal curve, temperatures are close to average. If observed temperatures
approach the red dotted record highs, it is as hot as it has ever been.
Observed temperatures near the blue-dotted record lows correspond to temperatures close
to the lowest ever encountered. For extended periods of record-setting high or low temperatures, there still will be considerable temperature variation throughout the day. Nighttime temperatures during these periods will be well below the record-high temperature for the entire day. However, when the cyclic variation of temperatures is taken into account, they still will be above the red-dotted curve of the highest temperatures during the generally cooler hours of nighttime. Isolated temperature measurements do not allow this comparison. The charts put observed temperatures in proper context with historical normal temperatures, high temperatures, and low temperatures throughout the daily temperature cycle. The charts also give an overall assessment for the question, "Has it generally been warmer or cooler recently than normal?" Answering this question means ignoring hourly temperature excursions and focusing on a longer average. The Deviation charts present this -- in green -- as an "average deviation" for the preceding two weeks, which is typically in the range of a few degrees. Charts are available for airports throughout the world.. Airports are used because they have excellent temperature data and long-term records. Normal temperatures, and the highest and lowest recorded temperatures, correspond to the airport's historical temperature record, which is typically 1950 to present. What the Charts ShowThe upper chart is a comparison of observed and normal temperatures. The past two weeks are at the left and a forecast for the next few days at the right. The most recent observed temperature is highlighted with a yellow dot to separate actual observations from forecast temperatures, and forecast temperatures are shown dashed. The color coding is as follows: |
 Observed Normal Record High Record Low |
| The lower chart shows the deviations of the observed temperature from normal. The average deviation is an average of the deviations for the past two weeks. The forecast deviations for the next few days are shown in a dotted pattern to help distinguish them from observed deviations on the left. The color coding is as follows: |
 Above Normal Below Normal Average Deviation |
The Normal CurveThe normal curve -- the green curve in the upper temperature plot -- comes from the airport's historical temperature record, which is typically 1950 to present. There are two aspects to deriving the curve:1. The diurnal cycle shape and timing of the highs and lows, and 2. The normal high and low for a given day of the year, as well as the record high and record low for that day. The historical record usually has two distinct types of temperature data. There is typically a shorter period of at least a few years of hourly data, which allows "1" to be answered. However, for most of the record, only daily highs and lows are available. These are assessed every day without regard to the time at which they occurred. This record of daily highs and lows allows "2" to be answered. To obtain the diurnal shape and timing from the shorter hourly record, preprocessing for the temperature and deviation charts does the following: First, the entire hourly record is examined to determine the times and temperatures of the lows and highs, and the intervening warming half-cycles (from lows to highs) and cooling half-cycles (from highs to lows). The resultant set of low and high times is the only information available regarding typical times at which they occur. They do not happen at the same time on succeeding days within the same year. Neither do they occur at the same time for a given day of the year, but in different years. Instead, there is a distribution of times for any given year, and the average timing also varies throughout the year in an annual cycle. The set of low and high times from the hourly record is used to obtain this average timing, day by day throughout the year. During processing, these times provide the "initial guess" about the timing of lows and highs, but do not completely determine it, because of the distribution of timing just mentioned. More will be said later about how that is determined. It is probably not generally appreciated that there is not only a distribution of temperatures throughout any given day, but a distribution of the timing of the lows and highs as well. Next, to obtain the correct diurnal cycle shape for the airport, the sets of warming and cooling half-cycles are each examined. The first step is to normalize them all to the same timing extent and same temperature range. Thinking of the associated cosine "base" curve, the cooling half-cycles are normalized to extend from "normalized temperature" +1 to -1, over "normalized time" zero to pi. After first flipping the warming half-cycles "upside down", the same is done with them. All of the normalized warming half-cycles, and all of the normalized cooling half-cycles, are averaged over the normalized interval zero to pi, to form the actual observed diurnal cycle shape for the airport. Fourier analyses of these two observed curves then yield two Fourier series representing them. It is to be emphasized that these are the actual, observed diurnal cycle shapes for temperatures at the airport. The Fourier series include the first two dozen terms, and allow very, very good fits of the observed curves. Indeed, when plotted, the Fourier curve almost completely "hides" the observed curve underneath. There is a great deal of global variability in this shape from location to location. Each diurnal cycle shape has been determined specific to that particular airport. You may notice that the diurnal cycles are much more "saw tooth" in appearance than the "average" temperature curves you may be accustomed to seeing. That is because all of the rounding of such average curves comes from the variability of timing of the lows and highs from year to year. The normal curves of Daily Temperature Cycle are not that kind of average curve. Indeed, for the bulk of the record, it is simply not available: the record has only highs and lows, without any record of their timing, and not all of the intervening hourly temperatures. The next step in preprocessing is to address aspect "2" -- the normal high and low for a given day of the year. This uses the larger historical dataset for the station -- the set of highs and lows -- without regard to timing. Preprocessing simply averages all the highs in the record for a given day of the year to obtain the average high for that day, and similarly averages all the lows to determine the average low. While finding the averages, it keeps track of the highest and lowest values and determines in all six measures of the historical temperature range: 1. the minimum low for the day of the year in the historical record, 2. the mean low for the day, 3. the maximum low for the day, 4. the minimum high for the day, 5. the mean high for the day, and 6. the maximum high for the day. That concludes the preprocessing and provides the input data for the updating the airport temperatures each hour during processing itself. In summary, there are three "pieces" to the input data: the diurnal cycle shape as specified by the Fourier coefficients, the "initial, first-cut" timing for lows and highs for any given day of the year, and the min low, mean low, max low, min high, mean high, and max high for each day of the year. The way these are used during actual processing is as follows. Suppose, just to keep the description simple, the program has just "fixed" the low for the day, which typically occurs in the early hours of the morning. It will have just set the timing for the low, and will be looking to the next high, which typically occurs in mid-afternoon. It will continue the normal green curve from the time it just fixed for the low, from the mean low for the day, along the "warming" diurnal half-cycle. Similarly, it will continue the "record low" blue-dotted curve from that time and from the min low for the day. It will continue the "record high" red-dotted curve from that time and from the max low for the day. To start, it will use the "initial, first-cut" timing for the afternoon's high. However, as temperatures become available close to that high, it adjusts the timing of the "normal" curve to match the timing in the current day. It does this by minimizing the largest discrepancy between the current observed temperature, and the resultant timing-adjusted green normal curve, over half of the half-cycles both to the left and to the right of the afternoon high. The result of this processing is that the timing of the normal curve will generally "line up" with the timing of the normal curve. Note that this sort of adjustment of timing is necessary, because the recorded low and high temperatures have no associated timing. Indeed, they were recorded without regard to when they occurred during the day. We have to reconstruct the timing distribution. What we want is for the "normal" high -- no timing attached -- to match today's high. That's what the processing does. Or, to look at it another way, we need to reconstruct the timing distribution of the lows and highs, and there is no better sample distribution to do that with than their actual, current, observed timing. If you follow the right edge of airport charts closely from hour to hour, you will see this adjustment of the normal curve timing taking place. High-Latitude StationsA word about locations near the earth's poles: perhaps somewhat surprisingly, these stations show considerable daily variation in temperature year-round. These are real temperatures from the record -- and, indeed, you can see the variability in observed temperatures. The most extreme example is Amundsen-Scott Station at the South Pole. Here, the sun stays at nearly the same angle throughout the day as it sweeps around the horizon, and only very slowly changes angle annually, disappearing below the horizon in winter. The daily variations thus are not caused by the changes in solar heating of lower latitudes as the sun rises and sets every day. If there were little daily temperature variability, the recorded temperatures would show little difference between daily highs and lows, but that is not the case in the real records. There is indeed a difference between them. Their timing, however, becomes more and more random the higher the latitude, and certainly in the darkness of winter at these locations. They apparently are due to air masses of slightly different temperature flowing past the station. The temperature and deviation charts approximate the random shape as closely as it can within its constraints of a true daily cycle, allowing up to a half-day variability in the placement of lows and highs. The South Pole station is an extreme case. Even at very-high latitude stations such as Qaanaak, Greenland, which is above the Arctic Circle, during months with at least some sunlight, the sun angle varies throughout the day and is higher in the sky at noon, and swings closer to it, or disappears below it, at night. Thus, the daily variation in solar heating gradually becomes larger as you move from the poles to the equator.LinksFor a list of available airports, click the following link: Location maps are also available for accessing the charts by clicking one of the following links: For a list of the historical recorded temperatures associated with each airport, click For long-term deviations by region of the world, click the following link: |
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